[Haskell-cafe] Categories (cont.)

[Tillmann Rendel]

Hi,

Christopher Howard wrote:
> instance Category ...

The Category class is rather restricted:

Restriction 1:
You cannot choose what the objects of the category are. Instead, the 
objects are always "all Haskell types". You cannot choose anything at 
all about the objects.

Restriction 2:
You cannot freely choose what the morphisms of the category are. 
Instead, the morphisms are always Haskell values. (To some degree, you 
can choose *which* values you want to use).


These restrictions disallow many categories. For example, the category 
where the objects are natural numbers and there is a morphism from m to 
n if m is greater than or equal to n cannot be expressed directly: 
Natural numbers are not Haskell types; and "is bigger than or equal to" 
is not a Haskell value.

   Tillmann